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Longshore Submerged Wave Breaker for a Reflecting Beach

Published online by Cambridge University Press:  28 May 2015

S. R. Pudjaprasetya*
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung, Indonesia, 40132
Elis Khatizah*
Mathematics Department, Bogor Agricultural University, Indonesia
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This paper considers the effect of a hard-wall beach on the downstream side of submerged parallel bars in a breakwater. In previous research, it was assumed that the beach can absorb all of the transmitted wave energy, when an optimal dimension for a submerged parallel bar is obtained and the wave amplitude is reduced as more bars are installed. However, for a hard-wall beach there are waves reflected from the beach that change the long-term wave interaction. We adopt the linear shallow water equations in Riemann invariant form and use the method of characteristics, in a procedure applicable to various formations of submerged rectangular bars. The distance from the parallel bar (or bars) to the beach determines the phase differences between right running waves in the beach basin and whether they superpose destructively or constructively before hitting the beach, to define the safest and the most dangerous cases. Our numerical calculations for one bar, two bars and for periodic rectangular bars confirm the analytical formulae obtained.

Research Article
Copyright © Global-Science Press 2012

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[1]Mei, C.C., Stiassnie, M., Yue, D.K.-P, Theory and Applications of Ocean Surface Waves, Advanced Series on Ocean Engineering Vol. 23, World Scientific, 2004.Google Scholar
[2]Pudjaprasetya, S. R. & Chendra, H.D., An optimal dimension of submerged parallel bars as a wave reflector, Bull. Malays. Math. Sci. Soc. (2), 32(1) (2009), pp. 5562.Google Scholar
[3]Wiryanto, L.H., Wave propagation over a submerged bar, ITB J. Sci., 42A(2) (2010), pp. 8190.Google Scholar
[4]Mattioli, F., Resonant reflection of a series of submerged breakwaters, Il Nuovo Comento, 13C(5) (1990), pp. 823833.CrossRefGoogle Scholar
[5]Heathershaw, A.D., Seabed-wave resonance and sandbar growth, Nature, 296 (1982), pp. 343345.CrossRefGoogle Scholar
[6]Davies, A.G. & Heathershaw, A.D., Surface wave propagation over sinusoidally varying topography, J. Fluid Mech., 144 (1984), pp. 419443.Google Scholar
[7]Yu, J. & Mei, C.C., Do longshore bars shelter the shore?, J. Fluid Mech. 404 (2000), pp. 251268.CrossRefGoogle Scholar
[8] Andonowati & Groesen, E. van, Similarities between optical and surface water waves, MIHMI, 8(3) (2002), pp. 18.Google Scholar
[9]Gisolf, D. & Verschuur, E., The Principles of Quantitative Acoustical Imaging, EAGE Publications, 2010.Google Scholar
[10]Hoffman, J.D., Numerical Methods for Engineers and Scientists, McGraw-Hill, Inc., 1992.Google Scholar
[11]Rey, V, Belzons, M., Guazzelli, E., Propagation of surface gravity waves over a retangular submerged bar, J. Fluid Mech., 235 (1992), pp. 453479.Google Scholar